A spherical black body with a radius of $24\;cm$ radiates $440\;W$ power at $500\;K$. If the radius were halved and the temperature doubled, the power radiated in watt would be
IIT 1997, Medium
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Radiated power by blackbody $P = \frac{Q}{t} = A\sigma {T^4}$ ==> $P \propto A{T^4}$$ \propto {r^2}{T^4}$
==> $\frac{{{P_1}}}{{{P_2}}} = {\left( {\frac{{{r_1}}}{{{r_2}}}} \right)^2}\,{\left( {\frac{{{T_1}}}{{{T_2}}}} \right)^4}$
==> $\frac{{440}}{{{P_2}}} = {\left( {\frac{{24}}{12}} \right)^2}\,{\left( {\frac{{500}}{{1000}}} \right)^4}$
==>${P_2} = 1760\,W$
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